Stars as Laboratories for Fundamental Physics - MPP Theory Group

Axions 535
otic heavy quarks: only the known fermions carry Peccei-Quinn charges.
Therefore, N is the number of standard families. Probably N = 3 so
that the remaining free parameters of this model are f a = f PQ /N and
x = f 1 /f 2 which is often parametrized by x = cot β or equivalently by
cos 2 β = x 2 /(x 2 + 1).
From a practical perspective, the main difference between the KSVZ
and DFSZ models is that in the latter axions couple to charged leptons
in addition to nucleons and photons. The former is an example for the
category of hadronic axion models.
Because f PQ ≫ f weak in these models, one may attempt to identify
f PQ with the grand unification scale f GUT ≈ 10 16 GeV (Wise, Georgi,
and Glashow 1981; Nilles and Raby 1982). However, the cosmological
bound f a ∼ < 10 12 GeV disfavors the GUT assignment. There exist
numerous other axion models, and many attempts to connect the PQ
scale with other scales—for a review see Kim (1987). In the absence
of a compelling model f a should be viewed as a free phenomenological
parameter.
14.3.2 Axion Mass and Coupling to Photons
The axion mass which arises from its mixing with π ◦ can be obtained
with the methods of current algebra to be (Bardeen and Tye 1978;
Kandaswamy, Salomonson, and Schechter 1978; Srednicki 1985; Georgi,
Kaplan, and Randall 1986; Peccei, Bardeen, and Yanagida 1987)
m a = f (
πm π z
f a (1 + z + w)(1 + z)
) 1/2
= 0.60 eV 107 GeV
f a
, (14.20)
where the quark mass ratios are (Gasser and Leutwyler 1982)
z ≡ m u /m d = 0.568 ± 0.042,
w ≡ m u /m s = 0.0290 ± 0.0043. (14.21)
Aside from these uncertainties there are higher-order corrections to
the current-algebra axion mass which have not been estimated in the
literature.